Finite degree formula for local volumes of klt pairs

Let $f\colon\big(y\in(Y,\Delta_Y)\big)\to\big(x\in(X,\Delta)\big)$ be a finite surjective morphism between klt pairs, and suppose it is crepant, meaning

$$f^*(K_X+\Delta)=K_Y+\Delta_Y.$$

Let $\widehat{\rm vol}(x,X,\Delta)$ denote the local volume of a klt pair. Finite degree formula conjecture.

$$\widehat{\rm vol}(y,Y,\Delta_Y)=\deg(f)\,\widehat{\rm vol}(x,X,\Delta).$$

This is a conjectural extension of the finite degree formula known in the source for certain morphisms; the stated arbitrary finite-surjective formulation is presented as needing resolution of the discrepancy with the known F-signature formula.